Let x and y be 3-digit numbers such that their difference is 729 and HCF is 81. What is the value of (x + y)?

1053

Let two numbers = 81x , 81y

⇒ 81 (x - y) = 729

⇒ (x - y) = 9

Both numbers are in three digit, then x = 12, 11 or 10 and y = 3, 2 or 1

Take= x = 11 and y = 2

Numbers are = 81 × 11, 81 × 2 = 891, 162

Sum of numbers are = 81 (11 + 2) = 81 × 13 = 1053